On average, males and females have the same median IQ of 100. This is a matter of test construction. IQ tests purposely eliminate questions that lead to sex biases in the score.

Males and females show average differences on subsections of IQ tests. Males are better on some sections, as spatial questions, while females are better on reading and some other verbal skills. The net result is that overall average IQ scores are calculated to balance out for males and females.

Another meaningful difference is in variance. Male IQ is more variable than female IQ. In other words, females tend to cluster around average scores, while males are somewhat more spread out, with more of them scoring at the very high end and the very low end of the IQ scales. This has been cited as a reason why more geniuses like Einstein or Mozart (and also school dropouts) are males.

The many male school dropouts make females seem more successful in high school. But in the workplace,

What he seems to have said is that the statistical distributions of the test scores of the sexes differ and that these differences may be, at least in part, biological.

That the scores differ is not disputed. For example, on the math SATs, the average boy's score is slightly higher than the average girl's score, but, perhaps more significantly, the variability of boys' scores is greater than that of girls' scores.

The Role of Variability

To appreciate the role of variability, we can imagine 1,000 women taking a math achievement test. Absurdly exaggerating for the sake of clarity, let's stipulate that 200 of them score around 75 on it, 600 of them score around 100, and 200 of them score around 125. In contrast, we can imagine 1,000 men taking the test, but now we stipulate that 200 of them score around 25 on it, 600 of them score around 100, and 200 of them score around 175.

Both groups' scores would average 100, but there is no doubt that the men would be disproportionately represented in institutions of higher learning as well as in institutions of other sorts.

Even with more realistic statistical distributions of talent in which women score at the very highest levels (and, of course, many do), the extremes and not the averages of the distribution often determine how many enter a technical field. Whatever the source and permanence of these distributional differences, nothing in them justifies any sort of discrimination against women, either as individuals or as a group.

So Why the Difference?

So what does bring about the difference in the distribution of scores? Psycho-social factors? Biological differences? Educational practices?

Undoubtedly social conditions play an important role. It can't be denied, for example, that sex discrimination, sometimes overt, but more often subtle, remains a serious problem in many places (especially in university hiring and promotion). Neither can it be denied that because of their socialization very many women simply have no interest in mathematics or science. There is some evidence that the abstraction of mathematics poses more of a social challenge for women than it does a cognitive challenge. For whatever reason women have a relatively greater preference for involvement with others.

And biological differences? Summers' remarks (or, rather, crude versions of them) caused an indignant uproar. But there are many biological differences between the sexes, and there is no reason why these should not extend to matters mathematical. In addition to the SAT and other test data, well-known studies have shown that across cultures and on average men do better in navigating through three-dimensional space and visualizing objects therein.

Other studies suggest that women are better at quick calculation and subitization, telling at a glance how many objects are lying about. Calling for the issue to be studied further does not make one a benighted sexist, and Summers, although he probably should have realized how his remarks would be taken, is certainly nothing of the sort.

Other Considerations

A marginally relevant point is that biological differences leading to a greater likelihood of mathematical talent are not always desirable. Autism and related disorders, for example, strike four times as many boys as girls, and there is some indication that a mild Asperger's syndrome, one of these related conditions, is not rare among research mathematicians.

Neither are psycho-social factors that lead to a greater likelihood of mathematical talent always desirable. It's anecdotal to be sure, but consider the behavior seemingly typical of many successful math and science graduate students. How appealing is subsisting on candy bars, take-out food and coffee while wearing the same clothes for days on end and focusing monomaniacally on some technical detail or other. And how appealing is the jockeying for dominance that often characterizes mathematical and scientific research. Again people vary in their tolerance for such conditions, but arguably proportionally fewer women than men will find them congenial.

Finally, even if it turns out that important biological differences underlie some of the difference in the distributions of mathematical talent, their effect may be quite small compared to the effect of these psycho-social factors. Vanderbilt professor Camilla Benbow, a specialist on gifted children, stresses the mutability of some of these factors. She points out that where there has been a concerted effort to encourage girls in mathematics, the ratio of mathematically high-achieving boys to mathematically high-achieving girls declines considerably.

The bottom line is that we can do much more to induce girls and women to study mathematics. We can make pedagogy and applications more palatable and stress the beauty and utility of the subject as well as its algorithms and calculations. Moreover, whether students of either sex go on to careers in science or not, there is compelling evidence that if they take more math, they will considerably increase their likelihood of finding higher-paying, more rewarding jobs.

- Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books, including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.